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On 02/27/2008 01:19 PM, Rick Tarara wrote:But the point is that at the 'conceptual' level we are NOT trying to formalize all this--just trying to convey a feeling for the consequences of special relativity. DOT PRODUCT--that's more than 'Greek to a liberal arts (or even Bio majors) intro class.
Thus, a first pass through SR with slow clocks etc. seems more reasonable to
me than immediately jumping into a more mathematical approach.
What's the evidence that the spacetime approach is "more mathematical"?
I see it as less mathematical, more pictorial, more analogical, more
physical.
If you go with "slow clocks etc." you need
-- slow clocks
-- shrunken rulers
-- funny mass
-- another funny mass
-- something to describe breakdown of simultaneity at a distance
... and by the time you formalize all of that, it's way more mathematical
than formalizing the structure of spacetime. Minkowski space has *one*
funny minus sign in the definition of the dot product, and that's it.
That's it! It couldn't possibly be simpler (without being trivial).
And it lends itself to drawing spacetime diagrams, which are helpful
for making all sorts of "paradoxes" disappear.